Before you read the lists of recommended emulators below, you should understand on this part of the webpage, underlined text (eg. Windows, etc.) is used to show the system the emulator runs on.
Linux
Mac OS X/OS X/macOS (most likely for Intel-based versions of Mac OS X, OS X and macOS)
MSX
Original PlayStation
Emulated system
Nintendo Entertainment System
Name of emulator
It Might be NES/imbNES
Where I recommend you download it
PlayStation Portable
Sega Saturn
Wii
Windows